9000031004
Level:
B
Assuming \(y\in \mathbb{R}\),
find the number of the solutions of the following algebraic equation.
\[
y^{4} + 5y^{2} + 6 = 0
\]
\(0\)
\(4\)
\(3\)
\(2\)
Higher degree equations and inequalities
9000028304
Level:
C
The following equation has solutions
\(x_1= 1\) and
\(x_2 = 3\). Find
the sum of the remaining real solutions.
\[
x^{4} - 12x^{3} + 47x^{2} - 72x + 36 = 0
\]
\(8\)
\(- 1\)
\(3\)
\(5\)
9000028305
Level:
C
The following equation has solution
\(x_1= 2\) and
\(x_2= 4\). Find
the sum of the remaining real solutions.
\[
x^{4} - 6x^{3} - x^{2} + 54x - 72 = 0
\]
\(0\)
\(- 1\)
\(1\)
\(2\)
9000028301
Level:
B
The following equation has a solution
\(x = 1\). Find
the sum of the remaining real solutions.
\[
x^{3} - 7x + 6 = 0
\]
\(- 1\)
\(1\)
\(0\)
\(2\)
9000028306
Level:
A
Find the sum of all real solutions of the following equation.
\[
\left (3 - x\right )\left (x^{2} - 4\right ) = 0
\]
\(3\)
\(0\)
\(2\)
\(5\)
9000028302
Level:
B
The following equation has a solution
\(x = 1\). Find
the sum of the remaining real solutions.
\[
x^{3} + 2x^{2} - x - 2 = 0
\]
\(- 3\)
\(- 1\)
\(0\)
\(2\)
9000028303
Level:
B
The following equation has a solution
\(x = -2\). Find
the sum of the remaining real solutions.
\[
x^{3} + 3x^{2} - 18x - 40 = 0
\]
\(- 1\)
\(1\)
\(0\)
\(4\)
9000025805
Level:
A
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 1)(x + 2)(x - 3)
\]
\(f(x) < 0 \iff x\in (-\infty ;-2)\cup (-1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3}
{2}\right )\cup (1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3}
{2}\right )\cup (3;\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3}
{2};-1\right )\cup (3;\infty )\)
9000019805
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^{4} + 2x^{2} + 1 = 0
\]
\(\emptyset \)
\(\left \{-1;1\right \}\)
\(\left \{-2;2\right \}\)
\(\left \{0\right \}\)
9000019806
Level:
B
Find the smallest integer solution of the following equation.
\[
x^{4} - 2x^{3} - x^{2} + 2x = 0
\]
\(- 1\)
\(0\)
\(1\)
\(2\)